ZIMSEC A Level Statistics Descriptive Statistics questions

Question 1

A group of twenty people played a game. The frequency distribution of their scores is: score 1 with frequency 2, score 2 with frequency 5, score 4 with frequency 7, and score x with frequency 6. If the mean score is 5, what is the value of x?

Accepted Answer

10

Question 2

A group of twenty people played a game with scores 1, 2, 4 and 10, having frequencies 2, 5, 7 and 6 respectively (mean score 5). What is the variance of this distribution?

Accepted Answer

11.7

Question 3

The times to the nearest minute taken by 12 students to complete a task are: 43, 45, 46, 42, 48, 42, 46, 55, 47, 42, 41, 44. What is the median time, in minutes?

Accepted Answer

44.5

Question 4

The times to the nearest minute taken by 12 students to complete a task are: 43, 45, 46, 42, 48, 42, 46, 55, 47, 42, 41, 44. What is the interquartile range (Q3 minus Q1) of these times, in minutes?

Accepted Answer

4.5

Question 5

The times to the nearest minute taken by 12 students to complete a task are 43, 45, 46, 42, 48, 42, 46, 55, 47, 42, 41, 44, giving Q1 = 42, median = 44.5, and Q3 = 46.5 minutes (IQR = 4.5). The upper fence for outliers is Q3 + 1.5×IQR = 53.25 minutes. What can be concluded about the value 55 and the overall shape of the distribution?

Accepted Answer

55 exceeds the upper fence, so it is an outlier, and the distribution is positively skewed

Question 6

A method of collecting statistical data involves obtaining information from every single member of a population, rather than from a sample of it. What is this method of data collection called?

Accepted Answer

census

Question 7

In a survey of 100 athletes at a marathon, the amount of water taken, in litres, was recorded as: 0-0.5 litres by 8 athletes, 0.5-1.0 litres by 20 athletes, 1.0-1.5 litres by 29 athletes, 1.5-2.0 litres by 22 athletes, and 2.0-2.5 litres by 21 athletes. Using the midpoint of each class, what is the estimated mean amount of water taken, in litres?

Accepted Answer

1.39

Question 8

In a survey of 100 athletes at a marathon, the amount of water taken, in litres, was recorded as: 0-0.5 litres by 8 athletes, 0.5-1.0 litres by 20 athletes, 1.0-1.5 litres by 29 athletes, 1.5-2.0 litres by 22 athletes, and 2.0-2.5 litres by 21 athletes. Using the midpoint of each class and a mean of 1.39 litres, what is the estimated standard deviation of the amount of water taken, correct to 3 decimal places?

Accepted Answer

0.613

Question 9

A stem-and-leaf diagram of pocket money (in dollars) received by a group of girls is given below, with key 3|30 = \$3.30: Stem 0: 50 50 50 75 Stem 1: 00 00 00 50 75 Stem 2: 00 00 00 50 50 Stem 3: 00 25 30 75 Stem 4: 50 Stem 5: 50 What is the mean pocket money received, to the nearest cent?

Accepted Answer

$2.14

Question 10

Using the same pocket money data (20 girls, values in cents: 50,50,50,75,100,100,100,150,175,200,200,200,250,250,300,325,330,375,450,550, mean \$2.14), what is the standard deviation, to the nearest cent?

Accepted Answer

$1.37

Question 11

The table below shows the masses of 200 students measured to the nearest kg. | Mass (kg) | Number of students | | --- | --- | | 46-50 | 20 | | 51-55 | 60 | | 56-60 | 56 | | 61-65 | 35 | | 66-70 | 19 | | 71-75 | 10 | Using upper class boundaries, what is the cumulative number of students with mass 60.5 kg or less?

Accepted Answer

136

Descriptive Statistics Questions and Answers

Test yourself on this topic

A group of twenty people played a game. The frequency distribution of their scores is: score 1 with frequency 2, score 2 with frequency 5, score 4 with frequency 7, and score $x$ with frequency 6. If the mean score is 5, what is the value of $x$ ?

A method of collecting statistical data involves obtaining information from every single member of a population, rather than from a sample of it. What is this method of data collection called?

A stem-and-leaf diagram of pocket money (in dollars) received by a group of girls is given below, with key $3|30 = \$3.30$ : Stem 0: 50 50 50 75 Stem 1: 00 00 00 50 75 Stem 2: 00 00 00 50 50 Stem 3: 00 25 30 75 Stem 4: 50 Stem 5: 50 What is the mean pocket money received, to the nearest cent?

A group of twenty people played a game with scores 1, 2, 4 and 10, having frequencies 2, 5, 7 and 6 respectively (mean score 5). What is the variance of this distribution?

Using the same pocket money data (20 girls, values in cents: 50,50,50,75,100,100,100,150,175,200,200,200,250,250,300,325,330,375,450,550, mean \$2.14), what is the standard deviation, to the nearest cent?

The times to the nearest minute taken by 12 students to complete a task are: 43, 45, 46, 42, 48, 42, 46, 55, 47, 42, 41, 44. What is the median time, in minutes?

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Descriptive Statistics Questions and Answers

Test yourself on this topic

A group of twenty people played a game. The frequency distribution of their scores is: score 1 with frequency 2, score 2 with frequency 5, score 4 with frequency 7, and score xxx with frequency 6. If the mean score is 5, what is the value of xxx?

A method of collecting statistical data involves obtaining information from every single member of a population, rather than from a sample of it. What is this method of data collection called?

A group of twenty people played a game with scores 1, 2, 4 and 10, having frequencies 2, 5, 7 and 6 respectively (mean score 5). What is the variance of this distribution?

Using the same pocket money data (20 girls, values in cents: 50,50,50,75,100,100,100,150,175,200,200,200,250,250,300,325,330,375,450,550, mean \$2.14), what is the standard deviation, to the nearest cent?

The times to the nearest minute taken by 12 students to complete a task are: 43, 45, 46, 42, 48, 42, 46, 55, 47, 42, 41, 44. What is the median time, in minutes?

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More topics in this subject

Practise this topic in the app

A group of twenty people played a game. The frequency distribution of their scores is: score 1 with frequency 2, score 2 with frequency 5, score 4 with frequency 7, and score $x$ with frequency 6. If the mean score is 5, what is the value of $x$ ?